Unified Variable Selection Of Varying Coefficient Model Based On Modal Regression

The variable coefficient model is a very important nonparametric regression model and has a wide range of applications in econometrics,biostatistics and social sciences.This paper studies the unified variable selection of the variable coefficient model and the uniform variable selection of the variable coefficient model under the missing data based on the mode of the majority regression.The content of this article mainly has the following two parts.The first part considers the uniform variable selection of the coefficients in the variable coefficient model under the modal regression.Firstly,the B-spline basis function is used to approximate the non-parametric function part of the variable coefficient model.The SCAD method is used to establish the penalty objective function to simultaneously select the relevant variables in the variable coefficient model and identify the covariates with constant effects.The progressive nature of the penalty estimator under some regular conditions proves that the uniform variable selection method has Oracle properties,and the proposed variable selection method is numerically simulated to evaluate its effectiveness.The second part discusses the robust uniform variable selection of the variable coefficient model in the case of random missing response variables.According to the modal regression and the imputation method to study the nonparametric estimation of the variable coefficient model,the penalty objective function is established by combining SCAD double punishment to achieve uniform variable selection,that is,selecting important variables in the variable coefficient model and identifying covariates with constant effects.The consistency and sparse property of the penalty estimation are verified under appropriate conditions.It is proved that the penalty estimate can simultaneously select the important variables in the variable coefficient model and identify the covariates with constant effects.Further,the method of adjusting the parameter selection is given and variable selection is achieved by the EM algorithm.Finally,some simulation comparisons are used to evaluate the effectiveness of the proposed method.The numerical simulation results verify the superior properties of the unified variable selection method.